The spaces $H^ p(B_ n), \;0<p<1,$ and $B_ {pq}(B_ n),\;0<p<q<1,$ are not locally convex
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- by Ji Huai Shi PDF
- Proc. Amer. Math. Soc. 103 (1988), 69-74 Request permission
Abstract:
In this note, we use the Ryll-Wojtaszczyk polynomials to prove that the spaces ${H^p}\left ( {{B_n}} \right ),0 < p < 1$, and ${B_{pq}}\left ( {{B_n}} \right ),0 < p < q < 1$, fail to be locally convex.References
- S. Bochner, Classes of holomorphic functions of several variables in circular domains, Proc. Nat. Acad. Sci. U.S.A. 46 (1960), 721β723. MR 120390, DOI 10.1073/pnas.46.5.721
- Arthur E. Livingston, The space $H^p,\ 0<p<1$, is not normable, Pacific J. Math. 3 (1953), 613β616. MR 56191, DOI 10.2140/pjm.1953.3.613
- Josephine Mitchell and Kyong T. Hahn, Representation of linear functionals in $H^{p}$ spaces over bounded symmetric domains in $C^{N}$, J. Math. Anal. Appl. 56 (1976), no.Β 2, 379β396. MR 427696, DOI 10.1016/0022-247X(76)90051-2
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-DΓΌsseldorf-Johannesburg, 1973. MR 0365062
- J. Ryll and P. Wojtaszczyk, On homogeneous polynomials on a complex ball, Trans. Amer. Math. Soc. 276 (1983), no.Β 1, 107β116. MR 684495, DOI 10.1090/S0002-9947-1983-0684495-9
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 69-74
- MSC: Primary 46E10; Secondary 32A35
- DOI: https://doi.org/10.1090/S0002-9939-1988-0938646-9
- MathSciNet review: 938646